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# Simplifying complex fractions

Learn how to take complex looking fractions and make them much, much simpler.

## Want to join the conversation?

• Why can't you swap the reciprocal fractions when multiplying?

When you turn the division problem into a multiplication by transforming the fraction on the right into the reciprocal of the fraction on the left, why can't you switch them around and make the fraction on top or on the left the reciprocal of the fraction on the right?
• It is kind of like saying 9 divided by 3, why cant we switch the numbers around and say 3 divided by 9. You can, but these two ways mean different things and you will get different answers. Hope this helps :)
• how do we simplify normal fractions tho
• It's defo a tricky thing to see until you get it like i just did lol but there's 2 ways you simplify fractions, first is the one where you Simplify by finding the Greatest Common Factor (GCF) for the numerator and denominator of your answer then divide them both by the GCF.

Then the other is where you Simplify an improper fraction into a mixed number by dividing the numerator (top number) by the denominator (bottom number), and you'll get a number with a remainder so you write the number as your whole number then write the remainder next to it, draw a line under it and write the original denominator of the fraction you just simplified under it.

You can find the GCF for both proper and improper fractions too to reduce the size of them, this is needed for bigger fractions especially when multiplying fractions and using prime factoring. That's if there is a GCF between the numerator and denominator, if it's not already at it's smallest possible fraction.

It becomes too hard and starts taking too long writing all the common factors when the numbers in your fractions start to get bigger.
• from to , Sal explains how to simplify 2/2/3. However, I could reason differently. I could simplify the 2/2, resulting in 1, and end up with 1/3. Their are other ways to get 1/3 too. I could break all the fractions to get 2÷2÷3, which I think could be 3 or 1/3 depending on how I look at it. How do I know which way I should do?
• How do u put the time he said it in the video in your question/ comment?? I need help plz!
(1 vote)
• So how would you do something like 1 / 1/2? Would it just be 1/2?
• if you mean (1/1)/2 then yes because 1/1 is 1 and that leaves 1/2.
If you meant 1/(1/2) then the answer is different:
with the last expression you are dividing 1 by 1/2, or in other words you are asking how many times does 1/2 fit into 1? Because we are dealing with very small numbers you can just count halves until you reach 1, in this case 2 halves go into 1 so your answer is 2. If you take a different approach that will work with any number you can use the rule that something divided by something else is the same as multiplying by its reciprocal. So 1/(1/2) = 1 x 2/1 = 2

hope it helped :)
• At why did he flip 3/7?
• Because that's what you when a fraction is being divided. If you want to multiply it, then flip the denominator.
• how do you do the simplify fraction work?
• I get how to simplify, but do you guys have anything that could help me solve the complex fractions. All I can find is simplifying complex fractions. I just want to solve them.
• Well you simplify like this...
for example 4/5 / 5/6 can be written as 4/5 divided by 5/6 so the answer is 24/25 and simplify fractions is the same as solving it.
Use this http://www.wikihow.com/Simplify-Complex-Fractions
• For 2x 3/2 why didn't he change 2 to 2/1?
(1 vote)
• Because it's not needed. It's an easy problem, doable with mental math.
• This math is my greatest foe. It's really Hard.
• Ill give you an idea about how to do it, I dont think its that effective though. It'll take time to understand

Lets say...

27/54

1. Find which times table both numbers occur in: 9
2. What does 9 need to be multiplied with to get to 27/54: 3 and 6